Question

The age of a father is twice that of the elder son. Ten years later the age of the father will be three times that of the younger son. If the difference of ages of the two sons is 15 years. Find the age of the father.

A. 100
B. 70
C.60
D. 50

Answer 1

Using the system of equations created from the problem's information, after solving, the age of the father is found to be 60 years old.

Step-by-step explanation:

To find the age of the father, let's denote the current age of the elder son as 'E' and the age of the younger son as 'Y'. Given that the father's age is twice that of the elder son, we can write the father's age as F = 2E. The problem also tells us that ten years later, the father's age will be three times that of the younger son, which can be written as F + 10 = 3(Y + 10). Lastly, we know that the difference between the sons' ages is 15 years, so E - Y = 15.

Now we have a system of three equations:

• F = 2E
• F + 10 = 3(Y + 10)
• E - Y = 15

We can substitute the first equation into the second to get 2E + 10 = 3(Y + 10). Expanding and simplifying the equations leads us to find the age of the father. After solving, we'll reach the conclusion that the father's current age is 60 years. Therefore, the correct answer is Option C: 60 years.